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1 2 3 Determination of flushing characteristics of the Irish Sea: a spatial approach 4 Tomasz Dabrowski, Michael Hartnett, Agnieszka I. Olbert 5 Civil Engineering Department / Ryan Institute for Environmental, Marine and Energy 6 Research, National University of Ireland, Galway. 7 8 9 Abstract 10 The Authors devised a novel generic approach to assessing the flushing of the Irish 11 Sea through the determination of spatially distributed residence times and the 12 development of flushing homogeneity curves. Results indicate that flushing of the 13 Irish Sea is both spatially and temporally highly variable. Average residence times 14 of the material introduced in winter may be up to 28% higher than the material 15 introduced in summer, and the aerial flushing deviation index may reach up to 470 16 days. The spatial approach to flushing is an extremely useful complement to 17 classical flushing analysis considering significant implications for management of 18 water quality. 19 20 Keywords: numerical modelling, Irish Sea, residence time, flushing, shelf seas, 21 thermohaline circulation 22 23 24 1. Introduction 25 Coastal waters remain under great threat from many aspects of human activity. 26 Cohen et al. (1997) estimate that about 50% of global population lives within the 27 coastal zone; much of the waste generated by these communities end in coastal 28 waters. Local hydrodynamic regimes of coastal waters are responsible for such 1 29 important issues as the distribution of effluents, transport of oil spills, sediments and 30 other materials. Many natural chemical, physical and biological processes occurring 31 within particular environments, including such important factors as low oxygen 32 levels or eutrophication, are influenced by circulation patterns. The knowledge of 33 hydrodynamic regimes in coastal waterbodies, being it ports and marinas, estuaries, 34 bays and larger coastal embayments, shelf seas, but also ocean basins, is therefore 35 desirable for engineers, scientists, managers and by policy makers. 36 An important physical attribute of each waterbody is the time scale characteristic 37 that describes its ability to renew water contained in it. In literature, it is most often 38 referred to as the flushing or residence time, (e.g. Bolin and Rodhe, 1973; 39 Zimmerman, 1976; Takeoka, 1984; Dyer, 1997; Luketina, 1998). Water circulation 40 in a given waterbody is a resultant of various forces, such as tide, wind and density 41 structure; knowledge of water renewal times can significantly aid the assessment of 42 the environmental state of waterbodies and their sustainable management. 43 The Irish Sea is a semi-enclosed shelf sea located between the islands of Ireland and 44 Great Britain, see Figure 1. Water circulation and associated water quality issues 45 concerning the Irish Sea have drawn the attention of more than a few researchers 46 over the past few decades (Ramster and Hill, 1969; Simpson and Hunter, 1974; 47 Proctor, 1981; Jefferies et al., 1982; Prandle, 1984; McKay and Baxter, 1985; 48 McKay and Pattenden, 1993; Hill et al., 1997; Horsburgh et al., 2000; Dabrowski 49 and Hartnett, 2008; Wang et al., 2008; Dabrowski et al., 2010). Being an area of 50 important fishery activities (Hill et al., 1996) and simultaneously exposed to effluent 51 discharges from multiple estuarine systems located on the Irish and British coasts as 52 well as from offshore outfalls and subject to further development of the marine 53 renewable energy sector, it is important that flow patterns and residence times 54 within the Irish Sea are well understood. 2 55 Hydrographically, the Irish Sea, located between 52-55N and 3-6W, is a complex 56 system where two tidal waves interact, and where wind and density-driven 57 circulations also play an important role. Flushing and transport of pollutants are not 58 well understood in the region. Previous efforts directed at estimation of the Irish Sea 59 residence times did not include the complexity of circulation (Jefferies et al., 1982; 60 Prandle, 1984; McKay and Baxter, 1985; McKay and Pattenden, 1993). Due to large 61 variations in the published values of residence times, the authors concluded that the 62 approach taking into account spatial variability of residence times is necessary. 63 For a more detailed description of the oceanography of the Irish Sea the reader is 64 referred to Bowden (1980). 65 In this paper, the objectives were to determine water renewal time scales in the Irish 66 Sea and to analyze complex flushing in the region. The methodology used by the 67 authors involves calculations of spatially distributed residence times and 68 development of the flushing homogeneity curves (FHC); the approach is based on 69 the application of a three-dimensional general ocean and coastal circulation and 70 transport model. This model was applied previously to the region to investigate 71 residence times in the eastern Irish Sea as well as travel times from the Sellafield’s 72 nuclear plant outfall site to various regions of the Irish Sea giving good agreement 73 with previously reported estimates (Dabrowski and Hartnett, 2008). The model was 74 also applied to examine the influence of the western Irish Sea gyre developing in 75 spring and summer on net flows, turn-over and residence times in the region 76 (Dabrowski et al., 2010). In this paper, the authors examine the complete Irish Sea 77 and also its three hydrographically diverse subregions, therefore the analysis of 78 spatial detail in residence times and development of FHC are required. The 79 advantage of using a numerical model for the purpose of the flushing properties 80 analysis is that it gives an additional insight into the impact of various physical 3 81 processes upon the derived water renewal time scale characteristic. Impacts can be 82 analyzed by excluding and including various forcing functions in the model. 83 The layout of the paper is as follows. Section 2 describes the methodology and 84 model setup, Section 3 provides a brief model calibration report followed by the 85 presentation and discussion of the results from the flushing simulations in Section 4, 86 before drawing final conclusions in Section 5. 87 88 2. Method 89 2.1. Model description 90 In this study, a three-dimensional numerical model, ECOMSED, was applied to 91 investigate water renewal time scales in the Irish Sea; the model is described in 92 detail in Blumberg and Mellor (1987). Below, the main features of the model and 93 details of its application to the Irish Sea are presented. 94 The bathymetry data of the Irish Sea was interpolated onto a 2 km rectangular finite 95 difference grid developed for the purpose of this study. The model domain is 96 delineated in Figure 1. Observations show that the density field in the Irish Sea is 97 controlled primarily by temperature from early summer onwards (Horsburgh, 1999). 98 For this reason, and due to the uncertainty in the salinity of inflowing oceanic water, 99 salinity was held constant at the open boundaries and set to climatologies. Tides 100 were imposed at the open sea boundaries as tidal constituents and the amplitudes 101 and phases of M2, S2, N2, K1, P1 and O1 constituents were provided. Freshwater 102 inputs along the British and Irish Coasts were included in the model and distributed 103 according to values provided in ISSG (1991). Sea temperatures at the open ocean 104 boundaries were specified at every computational time step, and the values were 105 obtained by a linear interpolation of monthly data from Meteorological Service 106 (1995) between the dates. A series of runs were performed to find an optimal surface 4 107 heat flux model among those incorporated within ECOMSED, as well as appropriate 108 parameter settings. 109 The bathymetry map is presented in Figure 1 along with the distribution of locations 110 where tidal elevations (T1-T14) and tidal currents (C1-C14) were available for the 111 model validation. 112 A full set of meteorological conditions was collated in order to perform seasonal 113 simulations. The calendar year of 1995 was chosen for simulations, which was 114 determined by data availability, and the fact that the existence of a well-established 115 western Irish Sea gyre in that year was already reported (Horsburgh, 1999). 116 Rationale for selecting this year for studying flushing properties of the Irish Sea is 117 discussed in more details in Dabrowski et al. (2010). Forcing data was obtained 118 from the US National Oceanic and Atmospheric Administration. This data originates 119 from the reanalysis/forecast system performing data assimilation using past data 120 from 1948 to the present. 121 The model solves the advection-diffusion equation to predict spatial distribution of 122 active (temperature and salinity) and passive tracers; MPDATA advection algorithm 123 developed by Smolarkiewicz (1984) has been applied. Horizontal diffusion is 124 calculated according to the formula developed by Smagorinsky (1963), which 125 adjusts the scale of mixing to the grid size. Horizontal Prandtl number, being the 126 ratio of horizontal viscosity to horizontal diffusivity, was held constant and set equal 127 to the recommended value of 1.0 (Hydroqual, 2002). The value of the Smagorinsky 128 coefficient was fixed at 0.1 as suggested by Mellor (2003). Small-scale mixing not 129 directly resolved by the model is parameterized in terms of horizontal mixing 130 coefficients. Turbulence closure scheme is based on the 2.5 level algebraic stress 131 equations developed by Mellor and Yamada (1982) with recent corrections 132 presented in Mellor (2001). Vertical Prandtl number, being the ratio of vertical 5 133 viscosity to vertical diffusivity, and the background mixing parameter were set equal 134 to the recommended values of 1.0 and 10-6 m2/s (Hydroqual, 2002), respectively. 135 The above settings proved to be successful in the reconstruction of the distribution 136 of Tc-99 (Olbert et al., 2010a, 2010b) and water temperatures in the Irish Sea 137 (Dabrowski et al., 2010; Olbert et al., 2011). 138 Further details on collated data can be found in Dabrowski (2005). 139 140 2.2. Water renewal time scale calculations 141 A concept of residence time derived in Takeoka (1984) was utilised in this study as 142 being the most suitable characteristic for describing exchange processes, when the 143 total material in a reservoir is considered. Takeoka (1984) introduced the remnant 144 function, r(t), as the ratio of the mass of material within a reservoir at a given time to 145 the initial mass of this material, and defined the average residence time, τr, as 146 follows: ∞ 147 τ r = ∫ r (t )dt (1) 0 148 Amongst the researchers who have utilised the above definition of the average 149 residence time was Murakami (1991), who developed a universal formula for the 150 remnant function, capable of representing the dye decay curves for basically any 151 reservoir with the tidal exchange: 152 r (t ) = exp(− A1t B1 ) = c(t ) c0 (2) 153 The empirical constants A1 and B1 depend on the shape of the decay curve and must 154 be determined for each case. An additional advantage of Murakami’s expression is 155 the fact that it can be easily integrated numerically giving the value of the residence 156 time of a studied reservoir. 6 157 It can be easily shown that under the assumption of complete mixing, the residence 158 time of a reservoir equals the time required to reduce the initial concentration of a 159 tracer by an exponential factor e, see for example van de Kreeke (1983) and Asselin 160 and Spaulding (1993). In this study, we treat individual numerical model’s cells as 161 completely mixed reactors, therefore we calculate the e-folding time, τe, of each cell 162 to compute the spatial distribution of residence time. 163 164 2.3. Summary of methodology 165 The three-dimensional ocean and coastal circulation and transport model was 166 applied to develop a barotropic and baroclinic model of the Irish Sea. Following its 167 calibration, passive tracer simulations were carried out to track spatial and temporal 168 distribution of the conservative tracer following its initial uniform distribution 169 throughout four regions presented in Figure 2. The tracer was introduced in the 170 model in the form of an instantaneous release and was uniformly dispersed 171 throughout the regions of interest. Four selected regions are distinct with regards to 172 the topographical features as well as the circulation patterns. Region A consists of 173 the entire Irish Sea. Region B is northern Irish Sea; this is a region of enhanced 174 fishery activity and its western section is subject to strong thermal stratification. 175 Region C covers the area of the St. George’s Channel only. It is the region of highly 176 energetic tidal circulation; it is vertically well mixed and is also bounded by strong 177 baroclinic features developing seasonally. Region D, the eastern Irish Sea, is 178 separated from the main channel running south-north; it is considerably shallower 179 and receives high input of contaminants from several major estuaries. 180 Dye decay curves, c(t)/c0 = f(t), obtained from the simulations were approximated 181 by the remnant function, r(t), equation (2), using the least squares method. 182 Integration of r(t), equation (1), yields the average residence times of the examined 7 183 regions. Calculated average residence times are representative of the entire regions, 184 i.e. tracer concentrations were averaged horizontally and vertically. Influence of 185 thermal stratification and associated baroclinic features developing in the Irish Sea, 186 such as the western Irish Sea gyre, which affects water exchange processes in the 187 region, has been a subject of a separate research presented in Dabrowski et al. 188 (2010). 189 Five flushing simulations for each region were carried out in this study; the 190 simulations differed in the tracer release date and forcing functions applied. Two 191 release dates were considered, summer (1st of June, runs F1 – F4) and winter (1st of 192 December, run F5), and four versions of the model comprised following forcing 193 functions: tides only (run F1), tides and wind stress (run F2), tides and heat fluxes 194 (run F3), tides, wind stress and heat fluxes (runs F4 and F5). A characterisation of 195 the simulations is presented in Table 1. 196 Finally, the e-folding times for each computational cell were computed and 197 presented as contour plots, showing the distribution of residence time with flushing 198 pathways clearly marked. On the basis of the spatial distribution of residence time, 199 FHC were developed summarising percentage area distribution of residence times 200 throughout the regions. The authors also proposed the aerial flushing deviation 201 index, FDI, as a useful measure of the spread in the values of distributed residence 202 times. FDI is the difference between the values of τe, τe90% and τe10%, for which 10% 203 of the area are characterised by greater and lower distributed residence times, 204 respectively. Therefore, FDI also represents the average slope of FHC. 205 206 3. Model Validation 207 The general tidal circulation in the Irish Sea predicted by the model follows the 208 pattern described in the literature (Bowden, 1980; ISSG, 1991). Contours of the 8 209 model-predicted depth-averaged tidal currents on a spring tide are presented in 210 Figure 3(a). The model reflects all features of the tidal circulation within the region 211 properly, for example strong currents in St.George’s and North Channels as well as 212 the area of persistent slack water to the east of the Isle of Man. The extents of the 213 regions of fast flow, exceeding 1.2 m/s, in the St. George’s, the North and the Bristol 214 Channels as well as the slack water in the Western Irish Sea are in close agreement 215 with the observations; see ISSG (1991). Magnification of tidal currents near 216 headlands was observed, as predicted by previous models (Horsburgh, 1999; 217 Proctor, 1981). An important feature from the point of view of this research work is 218 the model’s ability to predict locations of thermal fronts, with particular emphasis 219 placed on the western Irish Sea region, which stratifies during late spring and 220 summer each year. Simpson and Hunter (1974) proposed that the spatial pattern of 221 seasonal stratification is controlled by the distribution of tidal mixing as summarized 222 by the parameter H / v s3 , where H is the water depth, and vs is the maximum tidal 223 surface current. Figure 3(b) presents the spatial distribution of the log[ H / v s3 ] 224 parameter predicted by the model; contours of log[ H / v s3 ] = 2 , which according to 225 Simpson et al. (1977) determine the locations of thermal fronts, are labelled. The 226 spatial distribution of this parameter predicted by our model corresponds closely to 227 that observed by Simpson et al. (1977) in: the western Irish Sea, the southern 228 reaches of the St. George’s Channel as well as in Cardigan Bay to the east of the St. 229 George’s Channel. Comparisons of model-predicted and recorded tidal elevations at 230 selected coastal location (T14) and predicted and recorded currents over a tidal cycle 231 at location B3 in the western Irish Sea are also presented in Figure 3(c) and 3(d), 232 respectively. As can be seen, very good agreement with the observations has been 233 achieved for the barotropic component of the hydrodynamic model. The presented 9 234 comparisons are typical of the good correlation obtained between model predictions 235 and data for many locations throughout the Irish Sea. 236 Application of the heat flux model by Ahsan and Blumberg (1999) resulted in the 237 best correlation between the model-predicted temperatures and data used for 238 comparison. Sea surface temperatures at locations E1 and E2 were obtained from the 239 NOAA-CIRES CDC analysis/forecast system, whereas surface and nearbed 240 temperatures at location E3 were measured in-situ (Horsburgh, 1999); for locations 241 of E1 – E3 see Figure 4(a). 242 The model revealed particularly good capabilities to simulate proper values of 243 temperatures in the western Irish Sea region (E3) as presented in Figure 4(c), with R2 244 values of 95.6% and 96.0% for surface and nearbed temperatures, respectively (see 245 also Dabrowski et al. (2010) for more details). With regards to locations E1 and E2, 246 the R2 values averaged at 93.4% and 87.2%, respectively. The validation of the 247 model results against temperature in a stratified region of the Irish Sea is particularly 248 important due to the influence of thermal fronts on water circulation in the region. 249 Two other heat flux bulk formulae were tested as part of this study resulting in 250 slightly worse predictions when compared to data; for detailed intercomparison of 251 the performance of various heat flux models see Dabrowski (2005). 252 In the western Irish Sea cold relict water is preserved in a dome-like shape 253 throughout summer, as shown in Figure 4(b). The location of transect is shown in 254 Figure 4(a). Strong thermocline and horizontal thermal fronts are clearly visible; the 255 upper boundary of the dome is located approximately at 20 m depth below surface. 256 This temperature structure strictly corresponds to density structure; this result is 257 consistent with observations reporting the presence of colder, denser water lying 258 below 20 – 40 m water depth (Hill et al., 1997). 10 259 Since the dome is static, the sloping density surfaces bounding it can only be 260 maintained in geostrophic balance by cyclonic surface layer flow (Hill et al., 1997). 261 Recorded flows are typically between 5-10 cm/s and locally exceed 10 cm/s, and are 262 approximately front-parallel (Horsburgh et al., 2000). Figure 5(a) presents the 263 residual circulation reproduced by the model for mid-summer, when stratification is 264 well developed. As can be seen in Figure 5(a) the model successfully reproduces this 265 anticlockwise seasonal circulation and the magnitudes of the predicted baroclinic 266 currents are similar to those reported in Horsburgh et al. (2000). As can also be seen 267 in Figure 5(b), the barotropic only model does not predict such circulation in the 268 western Irish Sea region. 269 The reader is referred to Dabrowski (2005), Dabrowski et al. (2010), Olbert et al. 270 (2010a), Olbert et al. (2010b) and Olbert et al. (2011) for further details on the 271 model validation including validation of the advection-diffusion model (Olbert et al., 272 2010b). 273 274 275 4. Results and discussion of flushing analysis 276 Net flows through the Irish Sea have been discussed in Dabrowski et al. (2010) and 277 in more details in Dabrowski (2005). In this paper we concentrate on the 278 calculations of residence times and quantification of their spatial variabilities. 279 280 4.1. Residence times 281 The average residence times obtained for simulations F1-F5 carried out for regions 282 A-D are summarized in Table 1. 283 The results from the passive tracer transport simulations reveal a significant 284 variability in the values of the average residence time depending on the forcing 11 285 functions applied. Both baroclinic and wind induced currents proved to be largely 286 responsible for increased retention of water within the Irish Sea. The average 287 residence time of region A obtained in run F4 is greater by as much as 37% when 288 compared to the tidally only forced model (F1) and equals 386 days; thermohaline 289 circulation alone increases τr of region A by 24%, see Table 1 run F3. This shows 290 the retentive character of baroclinic circulation developing in the Irish Sea. Further 291 contribution towards increased retention of water in the Irish Sea is due to wind 292 driven circulation. Similar percentage increases apply also to regions B and C. 293 Region D, in turn, does not exhibit any significant variability in flushing rates, and, 294 as can be seen in Table 1, baroclinic circulation does not affect the residence time of 295 the region (run F3), whereas wind-induced circulation tends to reduce the residence 296 time only slightly. Region D is shallower than the remaining regions of the Irish Sea, 297 does not stratify in summer, and is located away from the main channel running 298 south-north through the Irish Sea, as indicated in Figure 1. Flushing of region D as 299 well as travel times from the Sellafield’s nuclear power plant outfall site located 300 within this region to various parts of the Irish Sea have been the subject of separate 301 research presented in Dabrowski and Hartnett (2008). 302 Also, as shown in Table 1, water contained within regions A-C on the 1st of 303 December, will have a greater residence time by about two months than that 304 contained there on the 1st of June. This is not surprising when the annual variation in 305 net flows through the Irish Sea is considered. Dabrowski et al. (2010) conclude that 306 the material contained within the Irish Sea in December will be initially transported 307 northward at high rates; however it will be returned to the regions over the next three 308 months as the flow reverses southward. In contrast, for the summer release the 309 northward transport is predicted for the first three months; the rates are significantly 310 lower when compared to those in December. It is followed by c.1.5 months of 12 311 southward transport, however the rates are low. The flow then reverses to northward 312 and the magnitude progresses quickly to high values in December. The above 313 pattern results in higher values of the residence time of water in regions A-C in the 314 case of winter release (F5) when compared to the summer release (F4). Since region 315 D is located beyond the main channel, it is not subject to the above variability and 316 thus the summer and winter residence times are virtually identical. 317 Previous estimates of residence times in the Irish Sea include those by Jefferies et al. 318 (1982), who used observed distributions of 137Cs and obtained the value 530 days for 319 region B. He also considered region D separately and calculated the residence time 320 of 290 days for this region. Further studies, carried out by McKay and Baxter (1985) 321 and McKay and Pattenden (1993), delivered significantly lower residence times of 322 region B of approximately 360 days. Values obtained by the authors of this research 323 are closer to the latter estimate and equal 263 and 338 days, for the summer and 324 winter tracer releases, respectively. Due to high spatial resolution in which transport 325 processes have been addressed in this study, the authors believe the proposed 326 estimates are more reliable. 327 328 4.2. Spatial distribution of residence time and flushing homogeneity curves 329 Spatial distributions of residence times in the domain, obtained using the 330 methodology described in Section 2.2, are presented in Figure 6. Fully forced 331 models were considered, therefore Figure 6 presents the results obtained from runs 332 F4 (summer release) and run F5 (winter release) in regions A-D. As far as the entire 333 region of the Irish Sea is concerned (region A), the St. George’s Channel is flushed 334 initially due to predominant northward flow in the case of both summer and winter 335 tracer releases, and backwater is formed in the eastern Irish Sea with the maximum 336 residence times predicted in the coastal waters near Liverpool. However, some 13 337 significant differences in flushing pathways between runs F4 and F5 are also 338 predicted. Waters adjacent to the Irish coast from c.50 km south of Dublin 339 northward are renewed considerably quicker in the event of the winter release (F5). 340 Tracer concentration in these waters drops below the e-fold value after about a year 341 following its introduction. Hence, it coincides with the predicted strong northward 342 drift, which is most likely responsible for faster tracer removal in this area. In the 343 case of the summer release, after the time period of 7 months southward flow is 344 predicted (see Dabrowski et al. (2010)), and also after one year the gyre in the 345 western Irish Sea is developed. Therefore, water is retained in the area from c.50km 346 south of Dublin northward for a longer time. Other differences in predicted 347 residence times include locations near the Welsh coast in the St.George’s Channel, 348 where higher values are predicted in the case of the winter tracer release. The 349 analysis of region B show that its western part is flushed significantly faster in both 350 F4 and F5 runs. The areas characterised by the greatest values of residence times are 351 in the south-east of the region, where backwater is formed. It can also be seen that 352 the western part of region B is flushed faster in the case of summer release when 353 compared to the winter release, due to a strong northward drift developing in the 354 Irish Sea in autumn (see Dabrowski et al. (2010)). High variability in flushing of 355 region C between the two runs is also apparent. Particularly interesting is also the 356 strong gradient of the residence time values between the southern and northern parts 357 of the region predicted by the model in run F5, including the Irish coastal areas As 358 far as region D is concerned, areas surrounding the Isle of Man are well flushed, and 359 introduced material stays for longer time mostly within south-east of the region in 360 the case of both summer and winter releases. In contrast to other regions, similarity 361 in the distribution of the residence time between the two runs is apparent. Only 14 362 slightly increased retention in case of the summer release can be noted. This fact is 363 also reflected in the values of the average residence times given in Table 1. 364 Flushing homogeneity curves for the examined region for the runs F4 and F5 are 365 presented in Figure 7. In general, the steeper the flushing homogeneity curve the less 366 variation in the values of residence times throughout the examined region. A 367 hypothetical completely mixed basin would yield vertical flushing homogeneity 368 curve. Figure 7 also confirms that there are significant differences in the spatial 369 distribution of residence time depending on the time of the tracer release. 370 As can be seen in Figure 7, 60% of region A has the values of residence time greater 371 than 500 days in the case of the summer release of tracer. Considering the winter 372 release, this value drops to around 35%. On the other hand, c.150 days are required 373 to renew water in the 10% of the area in the case of the summer release, whereas in 374 the case of the winter release this time doubles. Similarly for regions B and C, it can 375 be seen that the time required to flush the initial 10% of the area is significantly 376 higher in the case of the winter release. Since gradients of the curves following the 377 initial flushing of c.10% of the areas are similar, therefore it is concluded that this 378 initial time is the major contributor towards increased average residence times in the 379 case of winter releases. It can also be noted that region D differs in this regard: the 380 time required to flush the initial 10% of the area is slightly lower in the case of 381 winter release. Also, the curves are of similar shape and therefore the average 382 residence times of the region are virtually the same, as presented in Table 1. The 383 characteristic shapes of the curves indicate that although large parts of the regions 384 are characterised by similar values of residence times, there are also places where 385 sharp gradients in τe can be expected. This is represented by a characteristic ‘step’ 386 on the FHC; the most pronounced being on the FHC for region A and summer 387 release of tracer (see Figure 7(a)). Figure 7(a) shows that only a small percentage of 15 388 the area features τe between c.300 and c.500 days, and for τe of more than 500 days 389 the gradient of the curve is significantly greater. This characteristic ‘step’ indicates 390 that the domain is divided into slow and fast flushing systems, in relative terms and 391 that high gradient in the values of τe exist in the transition zone. This phenomenon 392 can be noted in Figure 6, and is particularly apparent in the case of summer release 393 in region A, where a sharp gradient is observed in the northern part of the St. 394 George’s Channel. It is worth noting that this divides energetic waters of the above 395 channel from relatively slack waters of the Western Irish Sea. 396 Table 2 summarizes FDI for each FHC presented in Figure 7. The higher the value 397 of the index the shallower the gradient of the curve and the greater the aerial 398 deviation from mean. The highest value of FDI of 470 days is observed for region A 399 and summer release (run F4), which is mainly due to the presence of sharp transition 400 zone from quickly to slowly flushed regions, reflected by a characteristic step on the 401 curve. FDI is significantly lower in the case of winter release indicating significant 402 temporal difference in flushing pathways in the region. FDI values for other regions 403 are lower (steeper curves) and less significant difference is observed for the two 404 tracer releases considered. Region C is characterised by the lowest values of FDI 405 and their summer and winter values are virtually the same, indicating similar 406 average slope of FHC. Interestingly, as presented in Table 1, τr of this region in the 407 case of winter tracer release is c.20% greater than in the case of summer release. It 408 can be therefore concluded that this notable increase in the value of τr is attributed to 409 the significant increase in the residence times of the quickest flushed areas. Indeed, 410 as can be seen in Figure 7, τe10% for this region increases from 105 days in the case 411 of summer release to 160 days in the case of winter release. 412 413 16 5 Summary and Conclusions 414 415 This paper presents details of research into developing a better understanding of the 416 assimilative capacity of the Irish Sea; a novel generic approach for flushing studies 417 has been proposed as part of this research. With regards to the Irish Sea modelling, 418 particular emphasis was put on the proper representation of thermal stratification 419 developing in the western Irish Sea during spring and summer. Flushing 420 characteristics considered include average residence time, spatially distributed 421 residence times, flushing homogeneity curve and flushing deviation index. 422 The main conclusions resulting from this research are summarized and discussed 423 below: 424 • This research illustrates that the proposed new approach using spatial 425 distribution of residence times and flushing homogeneity curves gives new 426 insight into flushing of the Irish Sea and transport processes. Since the Irish 427 Sea is a hydrographically complex system, a single value describing its 428 flushing properties delivers a picture that is incomplete. It has been shown 429 that even within hydrographically uniform subregions, further valuable 430 information is obtained through the adaptation of the proposed approach, 431 namely the compact visualisation of flushing pathways and quantification of 432 the variation in flushing. 433 • The authors showed that not only the average residence times of various 434 regions of the Irish Sea vary depending on the time of the year selected as 435 the start date for the examination of the water renewal processes, but spatial 436 distributions of residence times within these regions also differ. For example, 437 sharp gradients in the values of residence times are predicted in the case of 438 winter release that separate relatively quickly flushed St. George’s Channel 439 from the remaining relatively slowly flushed regions; the gradient is 17 440 significantly lower in the case of the summer release. Discrepancies within 441 the St. George’s Channel are also apparent when the region is considered 442 separately. Relatively small variation in flushing pathways between summer 443 and winter releases is observed in the eastern Irish Sea; this is consistent with 444 the results on average residence times, which reveal region’s stable flushing 445 properties. Thus, plotting the distributed residence times for a region gives a 446 second-order insight into the transport phenomena, and is therefore a useful 447 complement to flow fields provided by the hydrodynamic model along with 448 the general information provided by single values of average residence times. 449 • The concept of FHC was devised by the authors and then applied to 450 summarize flushing properties. FHCs provide useful generic information 451 about the degree of variation in flushing rates across the domain. In 452 particular, the range of the values of residence time is delivered as well as the 453 ‘smoothness’ of transition from quickly to slowly flushed regions. For 454 example, curves of shallow gradients indicate higher spatial variability in 455 residence times. Also, points of contraflexure and characteristic ‘step’ on the 456 curve indicate the presence of sharp gradients in flushing rates when moving 457 across the examined region, thus imposing careful management approach. 458 The average slope of the curve is quantified by FDI. Apart from bringing in 459 some more valuable information on the deviation in the values of residence 460 time from mean, further important conclusions in relation to slowest and 461 quickest flushed regions can be drawn when analysed in conjunction with τr. 462 For example, an increase of τr without change of FDI indicates an increase in 463 residence times of the quickest flushed regions. Therefore, FHC, FDI and τr 464 may be utilised in determining the need of more detailed studies of transport 465 and water renewal studies prior to making important management decisions. 18 466 • This research showed that average residence times of the Irish Sea and its 467 subregions are functions of tidal action, meteorological conditions and 468 density-driven currents, and thus also the time of the year considered. As far 469 as the entire region of the Irish Sea and summer tracer release are concerned, 470 tidal circulation alone flushes the domain in 282 days. When wind induced 471 flows are included, the average residence time increases to 322 days. Finally, 472 the average residence time of 386 days is computed when thermohaline 473 circulation is also included; this is 37% increase when compared to tidal 474 model. Regions B and C that were considered separately exhibit similar 475 response to various forcing functions applied. In the case of a winter tracer 476 release, further 15-28% increase in the values of average residence times is 477 observed, depending on the region. In contrast, the eastern Irish Sea (region 478 D) is characterised by relatively stable residence times. This significant 479 variation in flushing properties was then investigated in more details using 480 the new approach devised in this research. This is an extremely useful 481 approach considering significant implications for management of water 482 quality, particularly with regards to the discharge of persistent pollutants, 483 such as radionuclides. 484 485 Acknowledgements 486 The authors wish to acknowledge the Environmental Protection Agency, Ireland, for 487 funding this research project. 488 NCEP Reanalysis data provided by the NOAA-CIRES Climate Diagnostics Center, 489 Boulder, Colorado, USA, from their Web site at http://www.cdc.noaa.gov/. 490 UK Tide Gauge data and water currents records provided by the British 491 Oceanographic Data Centre, from their website at http://www.bodc.ac.uk. 19 492 493 494 References 495 496 Ahsan, A.K.M.Q., Blumberg A.F., 1999. Three-Dimensional Hydrothermal Model of Onondaga Lake, New York. Journal of Hydraulic Engineering 125(9), 912-923. 497 498 Asselin, S., Spaulding, M.L., 1993. Flushing times for the Providence River based on tracer experiments. 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A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. Journal of Computational Physics 54, 325-362. 603 604 Takeoka, H., 1984. Fundamental concepts of exchange and transport time scales in a coastal sea. Continental Shelf Research 3(3), 311-326. 605 606 van de Kreeke, J., 1983. Residence time: Application to small boat basins. Journal of Waterway, Port, Coastal, and Ocean Engineering 109(4), 416-428. 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 Wang, S., McGrath, R., Hanafin, J., Lynch, P., Semmler, T., Nolan, P., 2008. The impact of climate change on storm surges over Irish waters. Ocean Modelling 25, 83-94. Zimmerman, J.T.F., 1976. Mixing and flushing of tidal embayments in the western Dutch Wadden Sea: Part I. Distribution of salinity and calculation of mixing time scales. Netherland Journal of Sea Research 10(2), 149-191. List of Figures: Figure 1. The Irish Sea bathymetry and model orientation. Contours of 80 m water depth are highlighted to show the extents of the main channel. Distribution of the field data collected for the model set-up and calibration is also presented. Figure 2. Extents of the region of the Irish Sea selected for flushing studies. 22 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 Figure 3. Barotropic model validation: (a) maximum depth averaged tidal currents during an average spring tide, (b) distribution of tidal mixing ratio predicted by the model (see Simpson et al. (1977) for comparison, (c) comparison of modelled and recorded tidal elevations at T4 over a springneap tidal cycle and (d) measured and modelled current speeds at B3 over a tidal cycle. Figure 4. (a) Location of a transect and temperature stations E1-E3, (b) transverse section through the western Irish Sea showing modelled temperatures and (c) comparison of modelled and recorded temperatures at station E3. Figure 5. Residual circulation in the surface layer predicted by (a) barotropic and baroclinic model and (b) tidal model. Presented area is delineated in Figure 1. The extent of the western Irish Sea gyre is shown. Figure 6. Spatial distributions of residence times in regions A-D of the Irish Sea calculated from runs F4 and F5 of the model. Figure 7. Flushing homogeneity curves of regions A-D of the Irish Sea obtained from model runs (a) F4 and (b) F5. List of Tables: Table 1. Characterisation of model runs and values of calculated residence times. Table 2. Values of FDI for regions A-D and model runs F4 and F5. Figure 1. The Irish Sea bathymetry and model orientation. Contours of 80 m water depth are highlighted to show the extents of the main channel. Distribution of the field data collected for the model set-up and calibration is also presented. 23 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 A B C D Figure 2. Extents of the regions of the Irish Sea selected for flushing studies. 717 718 719 720 721 722 723 724 725 726 727 728 729 24 (a) (b) N 250.00 250.00 V [m/s] log[H/v 3S ] 200.00 200.00 2.00 150.00 1.60 100.00 Y [grid units] Y [grid units] 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 1.20 5.00 150.00 4.00 100.00 3.00 0.80 50.00 2.00 50.00 0.40 1.00 0.00 50.00 100.00 150.00 0.00 200.00 50.00 X [grid units] 100.00 150.00 200.00 X [grid units] Heysham (166,189) (c) 2 - 23 Fe bruary 1995 6 4 SSH [m] 2 0 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 data model -2 -4 -6 Time [hrs] 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 (d) Figure 3. Barotropic model validation: (a) maximum depth averaged tidal currents during an average spring tide, (b) distribution of tidal mixing ratio predicted by the model (see Simpson et al. (1977) for comparison, (c) comparison of modelled and recorded tidal elevations at T4 over a springneap tidal cycle and (d) measured and modelled current speeds at B3 over a tidal cycle. 25 (a) (b) N 250.00 E2 200.00 Y [grid units] 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 B3 E3 150.00 100.00 E1 50.00 50.00 100.00 150.00 200.00 X [grid units] (c) Figure 4. (a) Location of a transect and temperature stations E1-E3, (b) transverse section through the western Irish Sea showing modelled temperatures and (c) comparison of modelled and recorded temperatures at station E3. 26 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 (a) (b) Figure 5. Residual circulation in the surface layer predicted by (a) barotropic and baroclinic model and (b) tidal model. Presented area is delineated in Figure 1. The extent of the western Irish Sea gyre is shown. 27 873 874 875 Figure 6. Spatial distributions of residence times in regions A-D of the Irish Sea calculated from runs F4 and F5 of the model. 872 876 877 28 878 879 (a) 100 90 80 % area 70 region A 60 region B 50 region C 40 region D 30 20 10 0 0 100 200 300 400 500 600 700 800 τe greater than 880 881 (b) 100 90 80 70 region A % area 60 region B 50 region C 40 region D 30 20 10 0 0 100 200 300 400 500 600 700 800 τe greater than 882 883 884 885 886 887 888 889 Figure 7. Flushing homogeneity curves of regions A-D of the Irish Sea obtained from model runs (a) F4 and (b) F5. 890 Table 1. Characterisation of model runs and values of calculated residence times. Run characteristic Model run F1 F2 F3 Dye release date 01 Jun 01 Jun 01 Jun F4 01 Jun F5 01 Dec Model version tides only tides + wind tides + heat flux tides + wind + heat flux tides + wind + heat flux 29 Residence times for regions A-D τrA (d) 282 322 351 τrB (d) 214 219 257 τrC (d 154 179 179 τrD (d) 224 209 223 386 263 203 213 444 338 244 208 891 892 893 Table 2. Values of FDI for regions A-D and model runs F4 and F5. Model run F4 F5 FDIA (d) 470 330 FDIB (d) 215 245 894 895 896 897 898 30 FDIC (d) 145 155 FDID (d) 245 205